A probabilistic explanation for the size-effect in crystal plasticity

In this work, the well-known power-law relation between strength and sample size, d^-n, is derived from the knowledge that a dislocation network exhibits scale-free behaviour and the extreme value statistical properties of an arbitrary distribution of critical stresses. This approach yields n = (τ + 1)/(α +1), where α reflects the leading order algebraic exponent of the low-stress regime of the critical stress distribution and τ is the scaling exponent for intermittent plastic strain activity. This quite general derivation supports the experimental observation that the size effect paradigm is applicable to a wide range of materials, differing in crystal structure, internal microstructure and external sample geometry.